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Applications of fractional derivatives to nanofluids: exact and numerical solutions

In this article the idea of time fractional derivatives in Caputo sense is used to study memory effects on the behavior of nanofluids because some physical processes complex visco-elasticity, behavior of mechatronic and rheology are impossible to described by classical models. In present attempt hea...

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Main Authors: Zulkhibri, Ismail, Mohd Zuki, Salleh, Aman, Sidra, Khan, Ilyas
Format: Article
Language:English
Published: EDP Sciences 2018
Subjects:
QA Mathematics
Online Access:http://umpir.ump.edu.my/id/eprint/23900/1/Applications%20of%20fractional%20derivatives%20to%20nanofluids.%20Exact%20and%20numerical%20solutions.pdf
http://umpir.ump.edu.my/id/eprint/23900/
https://doi.org/10.1051/mmnp/2018013
https://doi.org/10.1051/mmnp/2018013
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spelling my.ump.umpir.239002019-10-18T02:34:06Z http://umpir.ump.edu.my/id/eprint/23900/ Applications of fractional derivatives to nanofluids: exact and numerical solutions Zulkhibri, Ismail Mohd Zuki, Salleh Aman, Sidra Khan, Ilyas QA Mathematics In this article the idea of time fractional derivatives in Caputo sense is used to study memory effects on the behavior of nanofluids because some physical processes complex visco-elasticity, behavior of mechatronic and rheology are impossible to described by classical models. In present attempt heat and mass transfer of nanofluids (sodium alginate (SA) carrier fluid with graphene nanoparticles) are tackled using fractional derivative approach. Exact solutions are determined for temperature, concentration and velocity field, and Nusselt number via Laplace transform technique. The obtained solutions are then expressed in terms of wright function or its fractional derivatives. Numerical solutions for velocity, temperature, concentration and Nusselt number are obtained using finite difference scheme. It is found that these solutions are significantly controlled by the variations of parameters including thermal Grashof number, fractional parameter and nanoparticles volume fraction. It is observed that rate of heat transfer increases with increasing nanoparticles volume fraction and Caputo time fractional parameters. EDP Sciences 2018 Article PeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/23900/1/Applications%20of%20fractional%20derivatives%20to%20nanofluids.%20Exact%20and%20numerical%20solutions.pdf Zulkhibri, Ismail and Mohd Zuki, Salleh and Aman, Sidra and Khan, Ilyas (2018) Applications of fractional derivatives to nanofluids: exact and numerical solutions. Mathematical Modelling of Natural Phenomena, 13 (1). pp. 1-12. ISSN 0973-5348 (Print); 1760-6101 (Online) https://doi.org/10.1051/mmnp/2018013 https://doi.org/10.1051/mmnp/2018013
institution Universiti Malaysia Pahang
building UMP Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Pahang
content_source UMP Institutional Repository
url_provider http://umpir.ump.edu.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Zulkhibri, Ismail
Mohd Zuki, Salleh
Aman, Sidra
Khan, Ilyas
Applications of fractional derivatives to nanofluids: exact and numerical solutions
description In this article the idea of time fractional derivatives in Caputo sense is used to study memory effects on the behavior of nanofluids because some physical processes complex visco-elasticity, behavior of mechatronic and rheology are impossible to described by classical models. In present attempt heat and mass transfer of nanofluids (sodium alginate (SA) carrier fluid with graphene nanoparticles) are tackled using fractional derivative approach. Exact solutions are determined for temperature, concentration and velocity field, and Nusselt number via Laplace transform technique. The obtained solutions are then expressed in terms of wright function or its fractional derivatives. Numerical solutions for velocity, temperature, concentration and Nusselt number are obtained using finite difference scheme. It is found that these solutions are significantly controlled by the variations of parameters including thermal Grashof number, fractional parameter and nanoparticles volume fraction. It is observed that rate of heat transfer increases with increasing nanoparticles volume fraction and Caputo time fractional parameters.
format Article
author Zulkhibri, Ismail
Mohd Zuki, Salleh
Aman, Sidra
Khan, Ilyas
author_facet Zulkhibri, Ismail
Mohd Zuki, Salleh
Aman, Sidra
Khan, Ilyas
author_sort Zulkhibri, Ismail
title Applications of fractional derivatives to nanofluids: exact and numerical solutions
title_short Applications of fractional derivatives to nanofluids: exact and numerical solutions
title_full Applications of fractional derivatives to nanofluids: exact and numerical solutions
title_fullStr Applications of fractional derivatives to nanofluids: exact and numerical solutions
title_full_unstemmed Applications of fractional derivatives to nanofluids: exact and numerical solutions
title_sort applications of fractional derivatives to nanofluids: exact and numerical solutions
publisher EDP Sciences
publishDate 2018
url http://umpir.ump.edu.my/id/eprint/23900/1/Applications%20of%20fractional%20derivatives%20to%20nanofluids.%20Exact%20and%20numerical%20solutions.pdf
http://umpir.ump.edu.my/id/eprint/23900/
https://doi.org/10.1051/mmnp/2018013
https://doi.org/10.1051/mmnp/2018013
_version_ 1648741145916735488
score 13.211869

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